Graph theory worksheet with answers

Free printable Graph theory worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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Name: ____________________   Date: ____________

1.Easy
ABCDE

Exactly one vertex of the graph has degree 4. Click it.

deg = 4
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
2.Easy

A simple graph has 5 vertices with degrees 4, 3, 2, 2, 1. How many edges |E| does it have?

deg: 4, 3, 2, 2, 1
|E| =
3.Medium

A tree has 4 vertices of degree 3, 3 vertices of degree 5, and all its other vertices are leaves (degree 1). How many leaves L does it have?

4 × deg 33 × deg 5
L =
4.Medium
ABCDEEuler circuitEuler path, no circuitneither

Does the connected graph have an Euler circuit, an Euler path that is not a circuit, or neither? Click your answer.

|V| = 5|E| = 5
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
5.Hard
71061416151114ABCDEFG

Use Dijkstra’s algorithm to find the length d(F) of the shortest path from A to F in the weighted graph.

start: Aend: F
d(F) =
6.Hard
41015262132ABCDEF

Use Dijkstra’s algorithm to find the length d(D) of the shortest path from A to D in the weighted graph.

start: Aend: D
d(D) =

Answer key

  1. 1. B
  2. 2. |E| = 6
  3. 3. L = 15
  4. 4. neither
  5. 5. d(F) = 31
  6. 6. d(D) = 6

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